Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber

Yang, Dan-Yu; Tian, Bo; Qu, Qi-Xing; Zhang, Chen-Rong; Chen, Su-Su; Wei, Cheng-Cheng

doi:10.1016/j.chaos.2020.110487

Cited by 106 publications

(20 citation statements)

References 35 publications

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“…• Making use of N -Soliton Solutions (5), we have constructed out the higher-order breather solutions for Eqn. (2), i.e., Solutions (18). Especially, we have presented the second-order breather solutions, i.e., Solutions (19).…”

Section: Discussionmentioning

confidence: 99%

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

et al. 2021

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Incompressible fluids are seen in ocean engineering, biomechanics, astrophysics, etc. A (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is hereby investigated. With the help of the Hirota method and symbolic computation, we present a bilinear auto-Bäcklund transformation with some analytic solutions. Based on the existing N -soliton solutions, we determine the higher-order breather solutions, where N is a positive integer. Via the Hirota-Riemann method, we derive the periodic-wave solutions. Graphical representations of the second-order breather and periodic waves are investigated. Moreover, we graphically present the second-order breather and periodic waves with the influence of the coefficients in that equation. Our results might be helpful to understand certain nonlinear phenomena in fluid mechanics.

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Section: Discussionmentioning

confidence: 99%

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

et al. 2021

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“…Exploring the localized solutions of certain nonlinear integrable partial differential equations is an active field of research in optics, plasma physics, astrophysics, oceanography and so on [1][2][3][4]. The solutions of nonlinear evolution equations, namely solitons, breathers, kinks, vortex solitons, dissipative solitons, oscillons, and rational solutions, model many real-world phenomena such as tsunami waves, rogue waves, tidal waves, cyclonic waves, waves in nonlinear optical fibers, shallow water waves and so on [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…3 t(α − 4bγ)Ω 22r = 1 + e 4a(x− x) + 2e 2a(x− x) { 1 + 32a 8 t 2 γ 2 + 2a 6 t 2 ( + 6bα + 9b 2 α 2 − 24b 3 αγ + 24b 4 γ 2 ) ) }…”

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Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity

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et al. 2022

Chaos, Solitons & Fractals

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“…The study of localized waves in nonlinear optical fiber using the variable coefficient equations have provided the theoretical basis for modern communication [30,31]. Motivated by the above considerations, a variable-coefficient coupled Hirota (VCCH) equation is studied in this work [32]:…”

Section: Introductionmentioning

confidence: 99%

Localized wave solutions to a variable-coefficient coupled Hirota equation in inhomogeneous optical fiber

et al. 2022

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Higher-order localized waves for a variable-coefficient coupled Hirota equation describes the vector optical pulses in inhomogeneous optical fiber and are investigated via generalized Darboux transformation in this work. Based on its Lax pair and seed solutions, the localized wave solutions are calculated, evolution plots are constructed, and the dynamics of the obtained localized waves are analyzed through numerical simulation. It is observed that the first-and second-order localized waves interact with dark-bright solitons or breathers, and the functions α(t), β(t), and δ(t) determine the propagation shape of the localized waves. The presented results contribute to enriching the dynamics of localized waves in inhomogeneous optical fiber.

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Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber

Cited by 106 publications

References 35 publications

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity

Localized wave solutions to a variable-coefficient coupled Hirota equation in inhomogeneous optical fiber

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